Exact Quantization of Multistage Stochastic Linear Problems
证明了任意成本分布的多阶段线性问题等价于有限情景树上的问题，通过分析多面体结构得到固定参数可解性等新复杂度结果。
We show that the multistage linear problem (MSLP) with an arbitrary cost distribution is equivalent to a MSLP on a finite scenario tree. We establish this exact quantization result by analyzing the polyhedral structure of MSLPs. In particular, we show that the expected cost-to-go functions are polyhedral and affine on the cells of a chamber complex, which is independent of the cost distribution. This leads to new complexity results, showing that MSLP is fixed-parameter tractable.